/*
Fast and Robust Detection of Crest Lineson Meshes C++ code
Copyright:(c) Shin Yoshizawa, 2004
E-mail: shin.yoshizawa@mpi-sb.mpg.de
URL: http://www.mpi-sb.mpg.de/~shin
Affiliation: Max-Planck-Institut fuer Informatik: Computer Graphics Group 
 Stuhlsatzenhausweg 85, 66123 Saarbruecken, Germany
 Phone +49 681 9325-408 Fax +49 681 9325-499 

 All right is reserved by Shin Yoshizawa.
This C++ sources are allowed for only primary user of 
research and educational purposes. Don't use secondary: copy, distribution, 
diversion, business purpose, and etc.. 
 */
#include<stdio.h>
#include<math.h>
#include"NRmacro.h"
#include"SvdSolve.h"
double SvdSolve::pythag(double a, double b)
{
	double absa,absb;
	absa=fabs(a);
	absb=fabs(b);
	if (absa > absb) return absa*sqrt(1.0+SQR(absb/absa));
	else return (absb == 0.0 ? 0.0 : absb*sqrt(1.0+SQR(absa/absb)));
}
void SvdSolve::svbksb(double **u,double *w,double **v,int m,int n, double b[],double x[]){
  int jj,j,i;
  double s;
  double *tmp = new double[n+1];
   for(j=1;j<=n;j++){
     s = 0.0;
     if(w[j]!=0.0){
       for(i=1;i<=m;i++)s += u[i][j]*b[i];
       s /= w[j];
     }
     tmp[j]=s;
   }
   for(j=1;j<=n;j++){
     s=0.0;
     for(jj=1;jj<=n;jj++)s += v[j][jj]*tmp[jj];
     x[j] = s;
   }
   delete [] tmp;
 }

void SvdSolve::svdcmp(double **a, int m, int n, double w[], double **v)
{
  //double pythag(double a, double b);
  int flag,i,its,j,jj,k,l,nm;
  double anorm,c,f,g,h,s,scale,x,y,z;
  double *rv1;

  rv1 = new double[(n+1)];//vector(1,n);
  for(i=0;i<=n;i++)rv1[i] = 0.0;
  g=scale=anorm=0.0;
  for (i=1;i<=n;i++) {
    l=i+1;
    rv1[i]=scale*g;
    g=s=scale=0.0;
    if (i <= m) {
      for (k=i;k<=m;k++) scale += fabs(a[k][i]);
      if (scale) {
	for (k=i;k<=m;k++) {
	  a[k][i] /= scale;
	  s += a[k][i]*a[k][i];
	}
	f=a[i][i];
	g = -SIGN(sqrt(s),f);
	h=f*g-s;
	a[i][i]=f-g;
	for (j=l;j<=n;j++) {
	  for (s=0.0,k=i;k<=m;k++) s += a[k][i]*a[k][j];
	  f=s/h;
	  for (k=i;k<=m;k++) a[k][j] += f*a[k][i];
	}
	for (k=i;k<=m;k++) a[k][i] *= scale;
      }
		}
    w[i]=scale*g;
    g=s=scale=0.0;
    if (i <= m && i != n) {
      for (k=l;k<=n;k++) scale += fabs(a[i][k]);
      if (scale) {
	for (k=l;k<=n;k++) {
	  a[i][k] /= scale;
	  s += a[i][k]*a[i][k];
	}
	f=a[i][l];
	g = -SIGN(sqrt(s),f);
	h=f*g-s;
	a[i][l]=f-g;
	for (k=l;k<=n;k++) rv1[k]=a[i][k]/h;
	for (j=l;j<=m;j++) {
	  for (s=0.0,k=l;k<=n;k++) s += a[j][k]*a[i][k];
	  for (k=l;k<=n;k++) a[j][k] += s*rv1[k];
	}
	for (k=l;k<=n;k++) a[i][k] *= scale;
      }
    }
    anorm=FMAX(anorm,(fabs(w[i])+fabs(rv1[i])));
  }
  for (i=n;i>=1;i--) {
    if (i < n) {
      if (g) {
	for (j=l;j<=n;j++)
	  v[j][i]=(a[i][j]/a[i][l])/g;
	for (j=l;j<=n;j++) {
	  for (s=0.0,k=l;k<=n;k++) s += a[i][k]*v[k][j];
	  for (k=l;k<=n;k++) v[k][j] += s*v[k][i];
	}
      }
      for (j=l;j<=n;j++) v[i][j]=v[j][i]=0.0;
    }
    v[i][i]=1.0;
    g=rv1[i];
    l=i;
  }
  for (i=IMIN(m,n);i>=1;i--) {
    l=i+1;
    g=w[i];
    for (j=l;j<=n;j++) a[i][j]=0.0;
    if (g) {
      g=1.0/g;
      for (j=l;j<=n;j++) {
	for (s=0.0,k=l;k<=m;k++) s += a[k][i]*a[k][j];
	f=(s/a[i][i])*g;
	for (k=i;k<=m;k++) a[k][j] += f*a[k][i];
      }
      for (j=i;j<=m;j++) a[j][i] *= g;
    } else for (j=i;j<=m;j++) a[j][i]=0.0;
    ++a[i][i];
  }
  for (k=n;k>=1;k--) {
    for (its=1;its<=30;its++) {
      flag=1;
      for (l=k;l>=1;l--) {
	nm=l-1;
	if ((double)(fabs(rv1[l])+anorm) == anorm) {
	  flag=0;
	  break;
	}
	if ((double)(fabs(w[nm])+anorm) == anorm) break;
      }
      if (flag) {
	c=0.0;
	s=1.0;
	for (i=l;i<=k;i++) {
	  f=s*rv1[i];
	  rv1[i]=c*rv1[i];
	  if ((double)(fabs(f)+anorm) == anorm) break;
	  g=w[i];
	  h=pythag(f,g);
	  w[i]=h;
	  h=1.0/h;
	  c=g*h;
	  s = -f*h;
	  for (j=1;j<=m;j++) {
	    y=a[j][nm];
	    z=a[j][i];
	    a[j][nm]=y*c+z*s;
	    a[j][i]=z*c-y*s;
	  }
	}
      }
      z=w[k];
      if (l == k) {
	if (z < 0.0) {
	  w[k] = -z;
	  for (j=1;j<=n;j++) v[j][k] = -v[j][k];
	}
	break;
      }
      if (its == 30) printf("no convergence in 30 svdcmp iterations\n");
      x=w[l];
      nm=k-1;
      y=w[nm];
      g=rv1[nm];
      h=rv1[k];
      f=((y-z)*(y+z)+(g-h)*(g+h))/(2.0*h*y);
      g=pythag(f,1.0);
      f=((x-z)*(x+z)+h*((y/(f+SIGN(g,f)))-h))/x;
      c=s=1.0;
      for (j=l;j<=nm;j++) {
	i=j+1;
	g=rv1[i];
	y=w[i];
	h=s*g;
	g=c*g;
	z=pythag(f,h);
	rv1[j]=z;
	c=f/z;
	s=h/z;
	f=x*c+g*s;
	g = g*c-x*s;
	h=y*s;
	y *= c;
	for (jj=1;jj<=n;jj++) {
	  x=v[jj][j];
	  z=v[jj][i];
	  v[jj][j]=x*c+z*s;
	  v[jj][i]=z*c-x*s;
	}
	z=pythag(f,h);
	w[j]=z;
	if (z) {
	  z=1.0/z;
	  c=f*z;
	  s=h*z;
	}
	f=c*g+s*y;
	x=c*y-s*g;
	for (jj=1;jj<=m;jj++) {
	  y=a[jj][j];
	  z=a[jj][i];
	  a[jj][j]=y*c+z*s;
	  a[jj][i]=z*c-y*s;
	}
      }
      rv1[l]=0.0;
      rv1[k]=f;
      w[k]=x;
    }
  }
  //free_vector(rv1,1,n);
  delete [] rv1;
}
